Bayesian strong gravitational-lens modelling on adaptive grids: objective detection of mass substructure in Galaxies

Abstract

We introduce a new adaptive and fully Bayesian grid-based method to model strong gravitational lenses with extended images. The primary goal of this method is to quantify the level of luminous and dark mass substructure in massive galaxies, through their effect on highly magnified arcs and Einstein rings. The method is adaptive on the source plane, where a Delaunay tessellation is defined according to the lens mapping of a regular grid on to the source plane. The Bayesian penalty function allows us to recover the best non-linear potential-model parameters and/or a grid-based potential correction and to objectively quantify the level of regularization for both the source and potential. In addition, we implement a Nested-Sampling technique to quantify the errors on all non-linear mass model parameters – marginalized over all source and regularization parameters – and allow an objective ranking of different potential models in terms of the marginalized evidence. In particular, we are interested in comparing very smooth lens mass models with ones that contain mass substructures. The algorithm has been tested on a range of simulated data sets, created from a model of a realistic lens system. One of the lens systems is characterized by a smooth potential with a power-law density profile, 12 include a Navarro, Frenk and White (NFW) dark matter substructure of different masses and at different positions and one contains two NFW dark substructures with the same mass but with different positions. Reconstruction of the source and lens potential for all of these systems shows the method is able, in a realistic scenario, to identify perturbations with masses ≳107 M⊙ when located on the Einstein ring. For positions both inside and outside of the ring, masses of at least 109 M⊙ are required (i.e. roughly the Einstein ring of the perturber needs to overlap with that of the main lens). Our method provides a fully novel and objective test of mass substructure in massive galaxies.